# Thread: Finding the trig expression

1. ## Finding the trig expression

Hi

I am having trouble getting the expression for the following:

1) Write$\displaystyle \frac{tan^2(x)+sec^2(x)}{tanxsec(x)}$ in terms of sin(x)

This is what i have done so far:

$\displaystyle \frac{tan^2(x)+(tan^2(x)+1)}{tanxsec(x)}$

$\displaystyle \frac{2tan^2(x)+1}{tanxsec(x)}$

This is where i get stuck, what should i do next?

P.S

2. Hello Paymemoney
Originally Posted by Paymemoney
Hi

I am having trouble getting the expression for the following:

1) Write$\displaystyle \frac{tan^2(x)+sec^2(x)}{tanxsec(x)}$ in terms of sin(x)

This is what i have done so far:

$\displaystyle \frac{tan^2(x)+(tan^2(x)+1)}{tanxsec(x)}$

$\displaystyle \frac{2tan^2(x)+1}{tanxsec(x)}$

This is where i get stuck, what should i do next?

P.S
Multiply top-and-bottom by $\displaystyle \cos^2x$, noting that $\displaystyle \tan x = \frac{\sin x}{\cos x}$ and $\displaystyle \sec x = \frac{1}{\cos x}$ :
$\displaystyle \frac{2\tan^2x+1}{\tan x\sec x}\times\frac{\cos^2x}{\cos^2x}$
$\displaystyle =\frac{2\sin^2x+\cos^2x}{\sin x}$

$\displaystyle =\frac{\sin^2x+1}{\sin x}$